# Philosophy:Antecedent (logic)

__: First half of an hypothetic statement (in logic)__

**Short description**An **antecedent** is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called the * protasis*.

^{[1]}

Examples:

- If [math]\displaystyle{ P }[/math], then [math]\displaystyle{ Q }[/math].

This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is **P**, and the consequent is **Q**. In an implication, if [math]\displaystyle{ \phi }[/math] implies [math]\displaystyle{ \psi }[/math] then [math]\displaystyle{ \phi }[/math] is called the **antecedent** and [math]\displaystyle{ \psi }[/math] is called the consequent.^{[2]} Antecedent and consequent are connected via logical connective to form a proposition.

- If [math]\displaystyle{ X }[/math] is a man, then [math]\displaystyle{ X }[/math] is mortal.

"[math]\displaystyle{ X }[/math] is a man" is the antecedent for this proposition while "[math]\displaystyle{ X }[/math] is mortal" is the consequent of the proposition.

- If men have walked on the Moon, then I am the king of France.

Here, "men have walked on the Moon" is the antecedent and "I am the king of France" is the consequent.

Let [math]\displaystyle{ y=x+1 }[/math].

- If [math]\displaystyle{ x=1 }[/math] then [math]\displaystyle{ y=2 }[/math],.

"[math]\displaystyle{ x=1 }[/math]" is the antecedent and "[math]\displaystyle{ y=2 }[/math]" is the consequent of this hypothetical proposition.

## See also

- Consequent
- Affirming the consequent (fallacy)
- Denying the antecedent (fallacy)
- Necessity and sufficiency

## References

- ↑ See Conditional sentence.
- ↑ Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004